hyrodium:Sorry for being late.I made two ways of graphical explanation of Euler’s formula.This

hyrodium:Sorry for being late.I made two ways of graphical explanation of Euler’s formula.This explanation is the same as wikipedia.Another explanation post is here.Fig 1The N-th power of a (complex number) is located as shown, and all triangles are similarity. because the absolute values are multiplied and the arguments are added to yield the polar form of the product. the points are on a logarithmic spiral.Fig 2Put a=(1+i θ/N), and take a limit N→∞ then the logarithmic spiral approaches the unit circle. The argument of a is equal to arctan(θ/N). This argument is approximately equal to θ/N in case of N>>1.Fig 3The N-th power of a is located as shown.Fig 4To sum up, take the limit N→∞ then a^N approaches cos(θ)+i sin(θ).Fig 5Remember the definition of e^z, We obtain Euler’s formula, e^i θ=cos(θ)+i sin(θ). -- source link
Tumblr Blog : hyrodium.tumblr.com

More pics about